Suppose there exists a compression function $F: \Sigma^k\times\Sigma^{c+m'} \rightarrow \Sigma^c$ with $m'>k$ such that $F$ is $(t',\epsilon')$-resistant to target collisions. Then there exists a compression function $H$ such that $H$ is $(t,\epsilon)$-resistant to target collisions for $t=t'- \Theta (k+m') $ and $\epsilon' = \epsilon + 2^{-k+1}$